Communication and Information Aggregation for Tricky Questions

We consider common-value voting in which a variable that is independent of the payoff-relevant state determines the meaning and precision of voters' private signals about the payoff-relevant state. Multiple senders sharing the same objective with the voters receive noisy signals that are contingent on the realized variable, and they send messages to the voters simultaneously. We show that by focusing on ``natural equilibria'', when the population of voters is sufficiently large, no information is transmitted by senders, and then information aggregation fails. We also propose a solution: if senders' messages are aggregated into binary levels, information transmission succeeds, and information is fully aggregated asymptotically.